My UVs are not in the same scale when I apply 'Average Island Scale'
It works with Areas

Average Island Scale is (to my kowledge) based on the 3D faces surface area, not it's dimensions. This would make more sense with more complex, irregular figures coming out from the unwrapping of a character, for example.

Take as instance the following example: two faces with the same area (1 square unit) and individual UV island. Running the operator doesn't affect the UV mapping in any way, wether the two figures have different dimension.

If I alter the scale of one of the two islands, and re-run the operator, all the selected faces are being scaled in order to show the correct ratio: they have the same surface in the 3D viewport, so their corresponding islands have the should cover the same area in the UV.



In the example you are providing, everything is going fine in my opinion. The portion with the trapezoidal face has less surface in the 3D viewport, so it should be smaller in the UV map.

If you would to get UV island that shares the same units, the faster way is to unwrap them at the same time (your figure n°3 is probably what you were looking for).